Characterizing polynomial and exponential complexity classes in elementary lambda-calculus

In this paper an implicit characterization of the complexity classes k-EXP and k-FEXP, for k≥0, is given, by a type assignment system for a stratified λ-calculus, where types for programs are witnesses of the corresponding complexity class. Types are formulae of Elementary Linear Logic (ELL), and the hierarchy of complexity classes k-EXP is characterized by a hierarchy of types.